Methods and apparatus for generating expanded code words to support error correction in a data communication system

A device comprising:

• a hardware expanded code word data encoder configured to
• obtain data to be encoded,
• obtain a first subset of bits of a first bit sequence,
• combine the data and the first subset of bits to generate a first combined bit sequence,
• apply an error correcting code to the first combined bit sequence to generate a first code word having a greater length than the first combined bit sequence,
• combine the first code word with the first bit sequence, resulting in first encoded data that includes both first parity information and the data, and
• repeat the applying and each combining with a second subset of bits of a second bit sequence, the second subset of bits being derived from the first subset of bits by:
• including a lowest single bit that has a same value as a lowest single bit of the first subset of bits;
• and
• including remaining higher bits each having a value that is a complement of the corresponding bit in the first subset of bits,
• the repetition resulting in second encoded data that includes both second parity information and the data, the second encoded data being based on a second code word generated by the error correcting code rather than the first code word, and
• a transmitter configured to transmit the first encoded data and the second encoded data to one or more target devices.

A non-transitory computer-readable medium comprising computer-executable instructions that, when executed, implement a system to:

• obtain data to be encoded;
• obtain a first subset of bits of a first bit sequence;
• combine the data and the first subset of bits to generate a first combined bit sequence;
• apply an error correcting code to the first combined bit sequence to generate a first code word having a greater length than the first combined bit sequence;
• combine the first code word with the first bit sequence, resulting in first encoded data that includes both first parity information and the data;
• and
• repeat the applying and each combining with a second subset of bits of a second bit sequence, the second subset of bits being derived from the first subset of bits by:
• including a lowest single bit that has a same value as a lowest single bit of the first subset of bits;
• and
• including remaining higher bits each having a value that is the complement of a corresponding bit in the first subset of bits,
• the repetition resulting in second encoded data that includes both second parity information and the data, the second encoded data being based on a second code word generated by the error correcting code rather than the first code word.